A Few Graphing Questions

[dragonrider]

Hello. I have a few questions about xy-coordinates.

1. I have an xy-coordinate system. O is the point of intersection, and A is a point (1, 2) on the line. I am supposed to choose from the following another point on line OA.
a. (0, 1)
b. (1, 3)
c. (2, 1)
d. (2, 4)
e. (4, 2)
How do I do this?

2. I have another xy-plane, this time with a parabola. The vertex (V) is (-2, -3) and the coordinate P is (-5, 3). I am supposed to select another point on the parabola.
a. (1, 1)
b. (1, 2)
c. (1, 3)
d. (2, 2)
e. (2, 3)
How do I do that?

3. I have a line with with six equally spaced tick marks. The second tick is labeled 1, the third x, and the fifth y. The question is "Which of the following expresses y in terms of x?"
a. x + 2
b. 2x + 1
c. 2x + 2
d. 3x - 2
e. 3x
How do I do this?

Thanks!

 

[Ishuda]

1. I have an xy-coordinate system. O is the point of intersection, and A is a point (1, 2) on the line. I am supposed to choose from the following another point on line OA.
I assume the point O is the origin (0,0). You need to learn the equation for a line passing through two points (x0, y0) and (x1, y1):
y = y0 + m (x-x0)
m = $\displaystyle \frac{y1 - y0}{x1-x0}$


2. I have another xy-plane, this time with a parabola. The vertex (V) is (-2, -3) and the coordinate P is (-5, 3). I am supposed to select another point on the parabola.
Again, you need to learn a standard for for a parabola with vertex (x0, y0)
y = y0 + a (x-x0)²
where a is some constant. Since you are given another point on the parabola, plug that point into the formula to find the value of a.


3. I have a line with with six equally spaced tick marks. The second tick is labeled 1, the third x, and the fifth y. The question is "Which of the following expresses y in terms of x?"
It seem to me this question is open to interpretation but, as I understand it, since the first tick mark is labeled 1, we can take each tick mark as being 0.5. Thus x = 1.5 and y 2.5 and a line passing through that point is
y = 2.5 + m (x - 1.5) = 2.5 - 1.5 m + m x.
Looking at the equations, if m were 1 what would 2.5 - 1.5 m be? What if m were 2? Or 3?

Or, to get rid of the 0.5 parts, let
m = (2 s + 1)
and we have
y = 2.5 + (2s+1) x - 3 s - 1.5 = 1 - 3 s + (2s+1) x
What about s=0? 1?

 

[dragonrider]

1. I have an xy-coordinate system. O is the point of intersection, and A is a point (1, 2) on the line. I am supposed to choose from the following another point on line OA.
I assume the point O is the origin (0,0). You need to learn the equation for a line passing through two points (x0, y0) and (x1, y1):
y = y0 + m (x-x0)
m = $\displaystyle \frac{y1 - y0}{x1-x0}$


2. I have another xy-plane, this time with a parabola. The vertex (V) is (-2, -3) and the coordinate P is (-5, 3). I am supposed to select another point on the parabola.
Again, you need to learn a standard for for a parabola with vertex (x0, y0)
y = y0 + a (x-x0)²
where a is some constant. Since you are given another point on the parabola, plug that point into the formula to find the value of a.


3. I have a line with with six equally spaced tick marks. The second tick is labeled 1, the third x, and the fifth y. The question is "Which of the following expresses y in terms of x?"
It seem to me this question is open to interpretation but, as I understand it, since the first tick mark is labeled 1, we can take each tick mark as being 0.5. Thus x = 1.5 and y 2.5 and a line passing through that point is
y = 2.5 + m (x - 1.5) = 2.5 - 1.5 m + m x.
Looking at the equations, if m were 1 what would 2.5 - 1.5 m be? What if m were 2? Or 3?

Or, to get rid of the 0.5 parts, let
m = (2 s + 1)
and we have
y = 2.5 + (2s+1) x - 3 s - 1.5 = 1 - 3 s + (2s+1) x
What about s=0? 1?

I'm sorry, but I'm not entirely sure what you mean. These were test questions I got incorrect, and the corrected test I was handed back had the answers.
1. d. (2, 4)
2. c. (1, 3)
3. d. 3x - 2

I never learned those equations and I am not sure how to apply them.

Here is a sketch of what the line looked like

 

[Ishuda]

I'm sorry, but I'm not entirely sure what you mean. These were test questions I got incorrect, and the corrected test I was handed back had the answers.
1. d. (2, 4)
2. c. (1, 3)
3. d. 3x - 2

I never learned those equations and I am not sure how to apply them.

Here is a sketch of what the line looked like
View attachment 4512

O.K. Let's take problem 1:
1. I have an xy-coordinate system. O is the point of intersection, and A is a point (1, 2) on the line. I am supposed to choose from the following another point on line OA.
a. (0, 1)
b. (1, 3)
c. (2, 1)
d. (2, 4)
e. (4, 2)
Again, assuming O is the origin, then the line goes through (0,0) and (1,2). Using the formula the equation for the line is
y = 2 x.
That is points on the line are of the form (x, y) = (x, 2x). Which point(s) in the list satisfy that relationship. Only choice d (2, 4) because it is (2, 2 * 2). No other point satisfies that relationship.

Similarly, for 2 you need to get the equation for the parabola and see what points in the list fit the equation. Since you know the vertex is at (-2, -3), the equation if
y = -2 + a (x + 3)²
Since the point (x,y) = (-5, 3) is on the line
3 = -2 + a (-5 + 3)²
Solve that for a and you will have the full equation.

Finally 3:
What is the form of the line
y = 2.5 + m (x - 1.5) = 2.5 - 1.5 m + m x
when m is equal to zero. Answer
y = 2.5
Does that look like any thing in the list?
What is the form when m =1? Does that look like anything in the list?
What about m = 2 or m = 3? We can stop there because the slope of the lines we can chose from is either 1, 2, or 3.

 

[dragonrider]

O.K. Let's take problem 1:
1. I have an xy-coordinate system. O is the point of intersection, and A is a point (1, 2) on the line. I am supposed to choose from the following another point on line OA.
a. (0, 1)
b. (1, 3)
c. (2, 1)
d. (2, 4)
e. (4, 2)
Again, assuming O is the origin, then the line goes through (0,0) and (1,2). Using the formula the equation for the line is
y = 2 x.
That is points on the line are of the form (x, y) = (x, 2x). Which point(s) in the list satisfy that relationship. Only choice d (2, 4) because it is (2, 2 * 2). No other point satisfies that relationship.

Similarly, for 2 you need to get the equation for the parabola and see what points in the list fit the equation. Since you know the vertex is at (-2, -3), the equation if
y = -2 + a (x + 3)²
Since the point (x,y) = (-5, 3) is on the line
3 = -2 + a (-5 + 3)²
Solve that for a and you will have the full equation.

Finally 3:
What is the form of the line
y = 2.5 + m (x - 1.5) = 2.5 - 1.5 m + m x
when m is equal to zero. Answer
y = 2.5
Does that look like any thing in the list?
What is the form when m =1? Does that look like anything in the list?
What about m = 2 or m = 3? We can stop there because the slope of the lines we can chose from is either 1, 2, or 3.

OK, I understand the first one now.
I'm a little foggy on the second one. I got a = 5/4. Do I plug that in now.
What is m in the third one?

 

[Ishuda]

OK, I understand the first one now.
I'm a little foggy on the second one. I got a = 5/4. Do I plug that in now.
What is m in the third one?

No 2:
Yes plug a = 5/4 back into the equation for the parabola. Then for each x in the list (the first number in the given pair) plug it into the equation and see what you get. If you get the second number in the list, that that choice satisfies the conditions and is (one of) the answer(s).

No. 3:
m is the slope of the line, that is the number multiplying x.

 

[dragonrider]

No 2:
Yes plug a = 5/4 back into the equation for the parabola. Then for each x in the list (the first number in the given pair) plug it into the equation and see what you get. If you get the second number in the list, that that choice satisfies the conditions and is (one of) the answer(s).

No. 3:
m is the slope of the line, that is the number multiplying x.

No. 2:
When I plugged in 1, I got 18, which is not one of the possible answers.

No. 3:
How do I find the slope? (Rise over run? How would I use that here?)

 

[Ishuda]

No. 2:
When I plugged in 1, I got 18, which is not one of the possible answers.
How about 2?
No. 3:
How do I find the slope? (Rise over run? How would I use that here?)
You have a choice of the slope in the answers. If any of them are correct, then the slope is either 1, 2, or 3.

-Ishuda

 

[dragonrider]

-Ishuda

Plugging in 2 got 31.25

 

[Ishuda]

Plugging in 2 got 31.25

The equation was wrong for 2, I swapped y and x. The equation should be
y = -3 + a (x + 2)²
so that

3 = -3 + a (-5 + 2)² = -3 + 9 a
or
a = 6/9 = 2/3
and
y = -3 + (2/3) (x + 2)²

y(1) = -3 + (2/3) 9 = -3 + 6 = 3 which is c
y(2) = -3 + (2/3) 16 = -3 +11 - (1/3) = 7 + (2/3) which is not in the list.
So the answer is c (1, 3)

You need to practice some of these problems so you know the standard forms and how to derive them.